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Force of magnetic attraction between hemispheres

  1. Nov 9, 2017 #1
    1. The problem statement, all variables and given/known data

    Calculate the force of magnetic attraction between the northern and southern hemispheres of a uniformly charged spinning spherical shell, with radius R, angular velocity ω and surface charge density σ.

    2. Relevant equations
    Maxwell Tensor : Tm =
    (1/μ) * ((B*n)B - (1/2)*B2 n)

    B_in =
    (2/3)*μσRω*z
    B_out =
    μm/(4πr3) * (2cosθ r + sinθ θ)
    where
    m = (4/3)*πR3(σωR)



    3. The attempt at a solution
    I do see in my solution that :
    1-We use a surface consisting of the entire equatorial plane, CLOSING IT with a hemispherical surface at infinity where (since the field is zero out there) contribution is zero.
    for r>R :
    B = μm/(4πr3) θ = - μm/(4πr3) z (Why ?! )
    2-
    We have a equatorial circular disk. We use B inside and da = rdrdφ. Direction is in z-axis!
    I don't want the solution because I already have it but MY QUESTIONS are :

    A) How should think and imagine this spheres ?!
    Should I think like this and use those formulas :
    sphere%202.jpg




    B) Why we do write B = μm/(4πr3) θ = - μm/(4πr3) z
    Why is θ =-z in this case ?! I dont get it !

    I know the rest. That is just integrating
     
  2. jcsd
  3. Nov 9, 2017 #2

    TSny

    User Avatar
    Homework Helper
    Gold Member

    I'm not quite following what you are asking here. Can you reword the question?

    It is because you are using spherical coordinates with θ measured from the positive z axis. The unit vector θ points in the direction of increasing θ. For a point on the equatorial plane of the sphere, what is the direction of θ?
     
  4. Nov 10, 2017 #3
    I've got it !

    Thanks
     
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